To find the "maiden" (often called the geometric mean) of four numbers, \(a\), \(b\), \(c\), and \(d\), you calculate the fourth root of their product:

\[
\text{Geometric Mean} = \sqrt[4]{a \times b \times c \times d}
\]

Given the numbers 3, 4, 5, and 6:

\[
\text{Geometric Mean} = \sqrt[4]{3 \times 4 \times 5 \times 6}
\]

Let's calculate that.

\[
\text{Product} = 3 \times 4 \times 5 \times 6 = 360
\]

\[
\text{Geometric Mean} = \sqrt[4]{360} \approx 4.5
\]

So, the geometric mean (or "maiden") of the numbers 3, 4, 5, and 6 is approximately **4.5**.

Would you like more details or have any questions?

Here are some related questions:
1. How do you calculate the geometric mean for two numbers?
2. What is the difference between the arithmetic mean and geometric mean?
3. Can you use the geometric mean for negative numbers?
4. What are some applications of the geometric mean in real-world scenarios?
5. How would the geometric mean change if you added a fifth number?

**Tip:** The geometric mean is particularly useful in finding average rates of growth or in situations where the numbers are of different magnitudes.

Learn how to calculate the geometric mean of the numbers 3, 4, 5, and 6 with a step-by-step solution. This problem covers the arithmetic and geometric means, including the formula for the geometric mean. Suitable for high school students (Grades 9-12).

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